Sometimes combinations are very simple and yet very beautiful just because other players did not see it. I just wanted to post 3 diagrams with a following clue diagrams to each problem given so that our readers regardless of chess strenght will understand what i am trying to say. The clue actually is what have been foreseen by the master in an actual game.
The combination player thinks forward; he starts from the given position, and tries the forceful moves in his mind. - Emanuel Lasker
By positional play a master tries to prove and exploit true values, whereas by combinations he seeks to refute false values ... A combination produces an unexpected re-assessment of values. - Emanuel Lasker
In my games I have sometimes found a combination intuitively simply feeling that it must be there. Yet I was not able to translate my thought processes into normal human language. - Mikhail Tal
According to such great attacking players as Bronstein and Tal, most combinations are inspired by the player's memories of earlier games. - Pal Benko
It is a profound mistake to imagine that the art of combination depends only on natural talent, and that it cannot be learned. Every player knows that all (or almost all) combinations arise from a recollection of familiar elements. - Richard Reti
All the quotes were taken from http://www.chessquotes.com/topic-combinations
Feel the beauty and try not just to rely on calculations.
... Luth Mikael